Orthogonal Frequency Division Multiplexing (OFDM) is an access technique that is being used in wireless local area networks (WLAN), such as IEEE 802.11a, and IEEE802.11g, as well as in different standards for broadcast, such as Digital Video Broadcasting—Terrestrial (DVB-T), DVB—Handhelds (DVB-H), Terrestrial Digital Multimedia Broadcasting (T-DMB), and Digital Audio Broadcasting (DAB). It is also the chosen access technique for Universal Mobile Telecommunications System—Long Term Evolution (UMTS LTE), a telecommunication standard promulgated by the 3rd Generation Partnership Project (3GPP).
In OFDM, the data is transmitted in parallel on a number of sub-carriers, which may be efficiently implemented by using an inverse fast Fourier transform (IFFT) in the transmitter, and a fast Fourier transform (FFT) in the receiver. If the size of the FFT is N, then N samples at the output of the FFT are referred to as an OFDM-symbol (i.e. a frequency domain OFDM-symbol). Typical values of N may range from 64 (used in e.g. WLAN) to 8192 (used in e.g. DVB-T). Values outside this range may, however, also be applicable.
In wireless communication, there is often a discrepancy between the transmitted and the received signal. This discrepancy may typically be due to a multi-path channel and noise. A multi-path channel, over which the signal is transmitted, often introduces time-dispersion to the signal. This may have the effect that symbols transmitted at different instants of time will interfere with one another to a certain extent at the receiver. This phenomenon is commonly referred to as inter-symbol interference (ISI). In OFDM, a cyclic prefix (CP) may be used to mitigate, at least partly, any negative impact resulting from ISI.
An illustration of a transmitted OFDM-signal with cyclic prefixes is provided in FIG. 1. In the figure, it is illustrated how the CP 110 may be created by copying the last part 120 of an OFDM-symbol 130 output from the IFFT and appending the copy just before the symbol. Thus, a transmitted (time domain) OFDM-symbol comprises the actual OFDM-symbol (or the useful part of the OFDM-symbol) 130 and a CP 110.
At the receiver side, a part of the received signal corresponding to the CP may be discarded before the signal is demodulated by the FFT. The issue of determining which part of the signal should be discarded and which part should be input to the FFT is commonly referred to as time synchronization. Throughout the application, time-synchronization will be referred to as positioning or placement of an FFT-window. In FIG. 2, an illustration of a possible placement of the FFT-window 210 is shown. In FIG. 2, it is also illustrated that the initial part 230 of the CP 220 has been corrupted due to ISI.
In communication systems where high bandwidth efficiency is desired, it is an advantage to have an estimation of the communication channel. The estimation is commonly determined in a channel estimator in the receiver. Estimating the communication channel may comprise estimating the impulse response of the channel if the channel is estimated in the time domain. If the channel is estimated in the frequency domain, the estimation may comprise estimating the transfer function of the channel. When a communication system is based on, for example, direct-sequence spread spectrum (DSSS), as is the case in the UMTS standard for Wideband Code Division Multiple Access (WCDMA), the channel is typically estimated in the time domain. When a system is based on OFDM on the other hand, the channel may typically be estimated in the frequency domain.
Channel estimation is one of the most critical tasks within a communication receiver in order to obtain good performance. It is typically also one of the more computationally intensive tasks in the receiver.
One approach to enable channel estimation is to transmit one or more known symbols and use these symbols for channel estimation. The known symbols may be transmitted separately as is done on the Common PIlot CHannel (CPICH) of UMTS. The known symbols may also be transmitted among the actual data as is done in OFDM for UMTS-LTE. The known symbols are commonly referred to as pilot symbols or reference symbols.
FIG. 3 illustrates an example distribution of pilot symbols 310a-h within a time-frequency grid of transmitted signals in an OFDM-system. FIG. 3 illustrates example OFDM-signals before IFFT-processing in the transmitter. The corresponding time-frequency grid will be found in the receiver after FFT-processing. In FIG. 3, it may be noted that pilot symbols 310a and 310b are transmitted in OFDM-symbol 301, that OFDM-symbols 302, 303, and 304 do not comprise any pilot symbols, and that pilot symbols 310c and 310d are transmitted in OFDM-symbol 305. Furthermore, it may be noted that pilot symbols 310a and 310b are transmitted on different sub-carriers compared to pilot symbols 310a and 310b. 
When the channel has been estimated at the positions where there are pilot symbols available, using any known method for channel estimation, the channel may also be estimated at the other positions in the time-frequency grid. One way of performing this estimation is by means of interpolation in frequency and/or in time. For this purpose, finding a suitable interpolation filter, that may be used to interpolate between the channel estimates at the positions of the pilot symbols, may be an important part of the setting up the channel estimation process.
For interpolation in time, the filter may be chosen based on how fast the channel is changing in the time direction. This type of channel variation is commonly referred to as the Doppler spread of the channel. Similarly, for interpolation in frequency, the filter may be chosen based on how frequency selective the channel is. This channel variation in the frequency direction is caused by the delay spread of the channel. There is a linear relation between the delay spread of the channel and how selective the channel is.
If, for example, a Wiener filter is used for interpolation between the channel estimates at the pilot symbol positions, the filter parameters may be chosen based on the correlation function of the channel in both time and frequency. The correlation functions in time and frequency can be estimated from the Doppler spread and the delay spread respectively. Knowledge of the Doppler spread and the delay spread may also be useful for simpler channel estimation approaches. For example, the Doppler spread and the delay spread may be used to determine an appropriate amount of filtering for interpolation in time and frequency respectively.
Thus, it is important to have an accurate estimate of the Doppler spread and of the delay spread.
The delay spread of the channel may be obtained by estimating what the impulse response looks like. This may, for instance, include processing of the received signal prior to FFT-processing. Estimating the actual impulse response to accomplish a delay spread estimate may be a rather complex approach. If, for example, the delay spread estimate will only be used to determine an appropriate amount of filtering in the frequency direction, a relatively rough estimate of the delay spread often suffice, and it may be a waste of resources to apply a complex delay spread estimation process.
An estimate of the delay spread of the channel may alternatively be obtained by making use of the linear relationship mentioned above, which may result in less complex delay spread estimation procedures.
K. Witrisal “On estimating the RMS delay spread from the frequency-domain level crossing rate”, IEEE Commun. Letters, July 2001, pp. 287-289, discloses a method where this linear relationship was exploited by evaluating the number of crossings of a level of the amplitude of a transfer function. One problem encountered for algorithms that are based on estimating a level-crossing rate, so called level-crossing algorithms, is that the average power of the signal must be determined since the level should relate to this average power. Estimating the power may not necessarily be a complex operation. However, in case the average power, and thereby the level, is not estimated with sufficient accuracy, the accuracy of the delay spread estimate will be inferior.
U.S. 2006/0159203 A1 discloses a procedure of channel estimation in a transmission channel with memory. An operation of estimation of a delay spread comprises evaluation of a mean number of crossings of the real and imaginary parts of the channel transfer function. This approach is commonly referred to as a zero-crossing algorithm. It does not rely on an estimate of the average power, and is hence more robust than a level-crossing algorithm.
One problem with zero-crossing algorithms is that the delay spread may be biased, i.e. over-estimated or under-estimated, under certain circumstances. In particular over-estimation is known to be a problem. Thus, there is a need for accurate, low complex and robust methods and apparatuses for delay spread estimation.